Presume that the supply of money is $800. The transactions and speculative demand for
money functions are given below.

m1 = 0.25Y
msp = 200 – 4r

Determine the equation of the LM curve.

md = m1
+ msp

md = 0.25Y
+ 200 – 4r

In symmetry, md = ms

Therefore,

0.25Y + 200 – 4r = 800

0.25Y = 800 – 200
+ 4r

0.25Y = 600
+ 4r

Y = 600
+ 4r
0.25

Y = 2,400
+ 16r

Hence the function of Y = 2,400 + 16r.

Illustration 66

Presume the consumption and investment function as below:

C = 200
+ 0.75Y
I = 500 – 5r

Also presume that the money supply is $ 560. The money demand function is as below:

md = 0.25Y – 4r

Determine the equation of IS Curve

Determine the equation of the LM curve

Determine the concurrent symmetry for the IS Curve and LM curves

Solution

IS Equation is as follows:

Y = C
+ I

Y = 200
+ 0.75Y + 500 – 5r

Y – 0.75Y = 700 – 5r

0.25Y = 700 – 5r

Y = 700 – 5r
0.25

Y = 2,800 – 20r

LM Equation is as follows:

md = 0.25Y – 4r

ms = 560

In Symmetry,
md = ms

Therefore,

0.25Y – 4r = 560

0.25Y = 560 + 4r

Y = 560
+ 4r
0.25

Y = 2,240
+ 16r

Concurrent Equation for the IS Curve and LM curves are as follows:

IS = LM

2,800 – 20r = 2,240
+ 16r

2,800 – 2,240 = 32r

560 = 32r

r = 17.5%

Hence,

Y = 2,800 – (20
*17.5)

= 2,800 – 350

Y = 2,450

Concurrent symmetry for the IS Curve and LM curves subsists when Y = 2,450 and
r = 17.5%.

Illustration 67

Presume the consumption, investment and money demand and supply functions are as below:

C = 0.75Y

I = 215
million dollars – 0.25r

md = 0.25Y – 5r

ms = 160
million dollars

Ascertain the following:

The symmetry earnings and the interest rate

The symmetry earnings and the interest rate when self-governing investment enhances
to 270 million dollars.

Solution

Symmetry earnings and the interest rate are as below:

Symmetry of the IS Curve = Y
= C + I

Y = 0.75Y
+ 215– 5r

Y – 0.75Y = 215 – 5r

0.25Y = 215 – 5r

Y = 215 – 5r
0.25

Y = 860 – 20r

Equation of the LM curve is as follows:

In Symmetry, md = ms

Therefore,

0.25Y – 5r = 160

0.25Y = 160
+ 5r

Y = 160
+ 5r
0.25

Y = 640
+ 20r

Concurrent symmetry for the IS and LM curves are as below:

IS = LM

860 – 20r = 640
+ 20r

40r = 220

r = 5.5%

Y = 860 – 20r

= 860 – (20*5.5)

= 860 – 110

Y = 750

Concurrent symmetry for the IS and LM curves subsists when Y = 750 and r = 5.5%

The symmetry earnings and the interest rate when self governing investment
enhances to 270 million dollars and the equation of the new IS curve will be as
below:

Y = C
+ I

Y = 0.75Y
+ 270 – 0.25r

Y – 0.75Y = 270 – 0.25r

0.25Y = 270 – 0.25r

Y = 270 – 0.25r
0.25

Y = 1,080 – 1r

Equation of the LM curve:

Y = 640
+ 20r

Concurrent symmetry for the IS curve and LM curve:

IS = LM

1,080 – r = 640
+ 20r

21r = 440

r = 21%

Y = 1,080 – 21

Y = 1,059

Concurrent symmetry for the IS curve and LM curve subsists when Y = 1,059 and
r = 21%.

Illustration 68

Presume that the value of k is 0.25.

Determine the direction and volume of movement in the LM curve when,

The increase in the supply of money is $20 millions and

The decrease in the supply of money is $50 millions.

Solution

The direction and the volume of movement in the LM curve when the increase in the
supply of money is at $ 20 millions:

Volume of Movement in the LM curve:

1 *
20
0.25

= 80

As there is an enhancement in the supply of money, the LM curve will move to
the right.

The decrease and the volume o movement in the LM curve when the decrease
in the supply of money is $50 millions.

Volume of movement in the LM curve:

1 * 50
0.25

= 200

As there is a decrease in the supply of money, the LM curve will move to the
left.

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